4x²+4x+1=0
nature of roots
Answer (1)
We can use the discriminant (Δ) to determine the nature of the roots. The discriminant is given by the formula:Δ = b² - 4acwhere a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.In this case, a = 4, b = 4, and c = 1.So, Δ = (4)² - 4(4)(1) = 16 - 16 = 0Now, we can determine the nature of the roots based on the value of the discriminant:If Δ > 0, the equation has two distinct real roots.If Δ = 0, the equation has one real root (a repeated or double root).If Δ < 0, the equation has two complex roots (no real roots).Since Δ = 0, the quadratic equation 4x² + 4x + 1 = 0 has one real root (a repeated or double root).Final answer:Therefore, the nature of the roots is real and equal.
